The problem of natural convection in porous media is involved in various engineering applications ranging from geothermal energy, seawater intrusion, contaminant transport to the storage of nuclear and radioactive waste [1]}, [2]}, [3]}, [4]}. Typically, the problem behavior is characterized by the Rayleigh number (\(\mathrm {Ra}\) ), a dimensionless index indicating laminar or turbulent flow regimes. Additionally, an alteration in the fluid's temperature or concentration resulting in variations in fluid density and viscosity (i.e., formation heterogeneity) could, in turn, influence the fluid flow field through fingering instabilities [5]}. One of many practical examples of interest is the process of carbon dioxide (\(\mathrm {CO_2}\) ) sequestration in aquifers. Depending on system \(\mathrm {Ra}\)  and the formation heterogeneity, convective mixing can greatly accelerate \(\mathrm {CO_2}\)  dissolution during geologic carbon storage [6]}, [7]}.
